Pascal’s PrinciplesReported by Maria Danica C. De Villa

Outline:• History• Pascal’s Principle• Formula• Sample Problems

The principle was named after the French mathematician and philosopher Blaise Pascal who discovered it in the 1600s.

Pascal's law says that when the pressure at any point in a static fluid in a closed system is changed, the change in pressure will disperse equally throughout the fluid. That is, the pressure at a point far away from the region of change will change by the same amount as a point nearby.

This fundamental characteristic of fluids provides the foundation for hydraulic systems found in barbershop chairs, construction equipment, and the brakes in your car.

Because the force applied to the contained fluid is distributed throughout the system, you can multiply the applied force through this application of Pascal’s Principle in the following manner. Assume you have a closed container filled with an incompressible fluid with two pistons of differing areas, A1 and A2. If you apply a force, F1, to the piston of area A1, you create a pressure in the fluid which you can call P1.

Similarly, the pressure at the second piston, P2, must be equal to F2 divided by the area of the second piston, A2.

Since the pressure is transmitted equally throughout the fluid in all directions according to Pascal’s Principle, P1 must equal P2.

Rearranging to solve for F2, you find that F2 is increased by the ratio of the areas A2 over A1.

Therefore, you have effectively increased the applied force F1. In the hydraulic lift diagram shown on the previous page, the distance over which F1 is applied will be greater than the distance over which F2 is applied, by the exact same ratio as the force multiplier.

Question: A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m2. If the chair is attached to a piston of area 0.1 m2, how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.

Answer: To solve this problem, first determine the force applied to the larger piston.

If the maximum force on the chair is 1500N, you can now determine the maximum mass which can be lifted by recognizing that the force that must be overcome to lift the customer is the force of gravity, therefore the applied force on the customer must equal the force of gravity on the customer.

If the chair has a mass of 5 kilograms, the maximum mass of a customer in the chair must be 148 kg.

Question: A hydraulic system is used to lift a 2000-kg vehicle in an auto garage. If the vehicle sits on a piston of area 0.5 square meter, and a force is applied to a piston of area 0.03 square meters, what is the minimum force that must be applied to lift the vehicle?Answer:

Archimedes’ PrincipleReported by Maria Danica C. De Villa

Outline:• History• Archimedes Water Balance• Principle of floatation

Archimedes a Greek scientist discovered an important scientific law related to buoyancy. It can be expressed as ‘Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.’

As the story goes, Archimedes poured himself a warm bath one day, and when he got in he realized the level of the water went up. He then determined that the more of his body he put in the bath, the higher the water level went.

What is the Science Behind Archimedes Principle?

Water Balance (Creative Commons)He realized that an object immersed

in water always displaced a volume of water equal to its own volume. This formed the basis of his experiment because he understood that, if he divided the weight of an object by the volume of water displaced, he would know its density.

For a fully submerged object, Archimedes' principle can be reformulated as follows:

then inserted into the quotient of weights, which has been expanded by the mutual volume

yields the formula below. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes:

Sample problemA rectangular barge 300cm long

and 200 cm wide floats at the edge of a fresh water lake. A horse jumps into the barge and the barge sinks 12cm. How much does the horse weigh?

Volume = length x width x height = 300cm x 200cm x 12cm = 720, 000 cm3 of

displaced water

Density of freshwater = 1g/cm3

720, 000 cm3 = 720, 000 g

720, 000 g = 720 kg

The weight of the horse is 720 kg.

Principle of floatationArchimedes' principle shows buoyant

force and displacement of fluid. However, the concept of Archimedes' principle can be applied when considering why objects float. Proposition 5 of Archimedes' treatise On Floating Bodies states that:

Any floating object displaces its own weight of fluid.

— Archimedes of Syracuse

Consider a 1-ton block of solid iron. As iron is nearly eight times denser than water, it displaces only 1/8 ton of water when submerged, which is not enough to keep it afloat. Suppose the same iron block is reshaped into a bowl. It still weighs 1 ton, but when it is put in water, it displaces a greater volume of water than when it was a block. The deeper the iron bowl is immersed, the more water it displaces, and the greater the buoyant force acting on it.

When any boat displaces a weight of water equal to its own weight, it floats. This is often called the "principle of floatation": A floating object displaces a weight of fluid equal to its own weight. Every ship, submarine, and dirigible must be designed to displace a weight of fluid at least equal to its own weight. A 10,000-ton ship must be built wide enough to displace 10,000 tons of water before it sinks too deep in the water.

Thank you for listening!